All fluids are to some extent compressible but gases show significant changes in density if pressure and/or temperature is changed.
Some gas flows can be treated as being incompressible but the following cases involve appreciable changes:
(a) Velocities near or larger than speed of sound (i.e. M > 1)
(b) Large accelerations of gas
(c) Large changes in elevation (e.g. in Year 1 Fluid mechanics lectures)
(d) Natural convection - flows with heat transfer
Since for a perfect gas